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{\flomajor\f31500\fbidi \froman\fcharset0\fprq2{\*\panose 02020603050405020304}Times New Roman;}{\fdbmajor\f31501\fbidi \froman\fcharset0\fprq2{\*\panose 02020603050405020304}Times New Roman;}
{\fhimajor\f31502\fbidi \froman\fcharset0\fprq2{\*\panose 02040503050406030204}Cambria;}{\fbimajor\f31503\fbidi \froman\fcharset0\fprq2{\*\panose 02020603050405020304}Times New Roman;}
{\flominor\f31504\fbidi \froman\fcharset0\fprq2{\*\panose 02020603050405020304}Times New Roman;}{\fdbminor\f31505\fbidi \froman\fcharset0\fprq2{\*\panose 02020603050405020304}Times New Roman;}
{\fhiminor\f31506\fbidi \fswiss\fcharset0\fprq2{\*\panose 020f0502020204030204}Calibri;}{\fbiminor\f31507\fbidi \froman\fcharset0\fprq2{\*\panose 02020603050405020304}Times New Roman;}{\f39\fbidi \froman\fcharset238\fprq2 Times New Roman CE;}
{\f40\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr;}{\f42\fbidi \froman\fcharset161\fprq2 Times New Roman Greek;}{\f43\fbidi \froman\fcharset162\fprq2 Times New Roman Tur;}{\f44\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew);}
{\f45\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic);}{\f46\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic;}{\f47\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese);}{\f379\fbidi \froman\fcharset238\fprq2 Cambria Math CE;}
{\f380\fbidi \froman\fcharset204\fprq2 Cambria Math Cyr;}{\f382\fbidi \froman\fcharset161\fprq2 Cambria Math Greek;}{\f383\fbidi \froman\fcharset162\fprq2 Cambria Math Tur;}{\f386\fbidi \froman\fcharset186\fprq2 Cambria Math Baltic;}
{\flomajor\f31508\fbidi \froman\fcharset238\fprq2 Times New Roman CE;}{\flomajor\f31509\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr;}{\flomajor\f31511\fbidi \froman\fcharset161\fprq2 Times New Roman Greek;}
{\flomajor\f31512\fbidi \froman\fcharset162\fprq2 Times New Roman Tur;}{\flomajor\f31513\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew);}{\flomajor\f31514\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic);}
{\flomajor\f31515\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic;}{\flomajor\f31516\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese);}{\fdbmajor\f31518\fbidi \froman\fcharset238\fprq2 Times New Roman CE;}
{\fdbmajor\f31519\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr;}{\fdbmajor\f31521\fbidi \froman\fcharset161\fprq2 Times New Roman Greek;}{\fdbmajor\f31522\fbidi \froman\fcharset162\fprq2 Times New Roman Tur;}
{\fdbmajor\f31523\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew);}{\fdbmajor\f31524\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic);}{\fdbmajor\f31525\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic;}
{\fdbmajor\f31526\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese);}{\fhimajor\f31528\fbidi \froman\fcharset238\fprq2 Cambria CE;}{\fhimajor\f31529\fbidi \froman\fcharset204\fprq2 Cambria Cyr;}
{\fhimajor\f31531\fbidi \froman\fcharset161\fprq2 Cambria Greek;}{\fhimajor\f31532\fbidi \froman\fcharset162\fprq2 Cambria Tur;}{\fhimajor\f31535\fbidi \froman\fcharset186\fprq2 Cambria Baltic;}
{\fbimajor\f31538\fbidi \froman\fcharset238\fprq2 Times New Roman CE;}{\fbimajor\f31539\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr;}{\fbimajor\f31541\fbidi \froman\fcharset161\fprq2 Times New Roman Greek;}
{\fbimajor\f31542\fbidi \froman\fcharset162\fprq2 Times New Roman Tur;}{\fbimajor\f31543\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew);}{\fbimajor\f31544\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic);}
{\fbimajor\f31545\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic;}{\fbimajor\f31546\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese);}{\flominor\f31548\fbidi \froman\fcharset238\fprq2 Times New Roman CE;}
{\flominor\f31549\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr;}{\flominor\f31551\fbidi \froman\fcharset161\fprq2 Times New Roman Greek;}{\flominor\f31552\fbidi \froman\fcharset162\fprq2 Times New Roman Tur;}
{\flominor\f31553\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew);}{\flominor\f31554\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic);}{\flominor\f31555\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic;}
{\flominor\f31556\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese);}{\fdbminor\f31558\fbidi \froman\fcharset238\fprq2 Times New Roman CE;}{\fdbminor\f31559\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr;}
{\fdbminor\f31561\fbidi \froman\fcharset161\fprq2 Times New Roman Greek;}{\fdbminor\f31562\fbidi \froman\fcharset162\fprq2 Times New Roman Tur;}{\fdbminor\f31563\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew);}
{\fdbminor\f31564\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic);}{\fdbminor\f31565\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic;}{\fdbminor\f31566\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese);}
{\fhiminor\f31568\fbidi \fswiss\fcharset238\fprq2 Calibri CE;}{\fhiminor\f31569\fbidi \fswiss\fcharset204\fprq2 Calibri Cyr;}{\fhiminor\f31571\fbidi \fswiss\fcharset161\fprq2 Calibri Greek;}{\fhiminor\f31572\fbidi \fswiss\fcharset162\fprq2 Calibri Tur;}
{\fhiminor\f31575\fbidi \fswiss\fcharset186\fprq2 Calibri Baltic;}{\fbiminor\f31578\fbidi \froman\fcharset238\fprq2 Times New Roman CE;}{\fbiminor\f31579\fbidi \froman\fcharset204\fprq2 Times New Roman Cyr;}
{\fbiminor\f31581\fbidi \froman\fcharset161\fprq2 Times New Roman Greek;}{\fbiminor\f31582\fbidi \froman\fcharset162\fprq2 Times New Roman Tur;}{\fbiminor\f31583\fbidi \froman\fcharset177\fprq2 Times New Roman (Hebrew);}
{\fbiminor\f31584\fbidi \froman\fcharset178\fprq2 Times New Roman (Arabic);}{\fbiminor\f31585\fbidi \froman\fcharset186\fprq2 Times New Roman Baltic;}{\fbiminor\f31586\fbidi \froman\fcharset163\fprq2 Times New Roman (Vietnamese);}}
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\fs22\lang3082\langfe3082\loch\af31506\hich\af31506\dbch\af31505\cgrid\langnp3082\langfenp3082 {\rtlch\fcs1 \ab\af0\afs24 \ltrch\fcs0 \b\f0\fs24\cf2\insrsid2950479 \hich\af0\dbch\af31505\loch\f0 Maximum Likelihood Hebbian Learning}{\rtlch\fcs1 
\ab\af0\afs24 \ltrch\fcs0 \b\f0\fs24\cf13\insrsid2950479 
\par }\pard \ltrpar\qc \li0\ri0\sa200\sl276\slmult1\nowidctlpar\wrapdefault\faauto\rin0\lin0\itap0\pararsid2950479 {\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\insrsid2950479 
\par }\pard \ltrpar\qj \li0\ri0\sa200\sl276\slmult1\nowidctlpar\wrapdefault\faauto\rin0\lin0\itap0\pararsid14683089 {\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\insrsid13593770\charrsid14683089 \hich\af0\dbch\af31505\loch\f0 \hich\f0 
En este apartado presentamos una extensi\'f3\loch\f0 \hich\f0 n de las reglas de aprendizaje de Redes de An\'e1\loch\f0 lisis de Componentes Pr\hich\af0\dbch\af31505\loch\f0 \hich\f0 incipales (PCA), las cuales han sido derivadas para ser \'f3\loch\f0 
\hich\f0 ptimas para una funci\'f3\loch\f0 \hich\f0 n de densidad de probabilidad espec\'ed\loch\f0 \hich\f0 fica.  Esta familia completa de reglas de aprendizaje son m\'e9\loch\f0 \hich\f0 todos de desarrollo de B\'fa\loch\f0 
squeda Exploratoria de Proyecciones.}{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\insrsid2950479\charrsid14683089 
\par }{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\insrsid13593770\charrsid14683089 \hich\af0\dbch\af31505\loch\f0 Varias investigacio\hich\af0\dbch\af31505\loch\f0 \hich\f0 
nes han demostrado que las reglas de aprendizaje pueden derivar aproximadamente en una mejor l\'ed\loch\f0 \hich\f0 nea de comprensi\'f3\loch\f0 \hich\f0 n de los datos. Entonces podemos comenzar con la funci\'f3\loch\f0 n de coste:
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\par }{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\insrsid13593770\charrsid14683089 \hich\af0\dbch\af31505\loch\f0 \hich\f0 La cual vamos a minimizar para conseguir la actualizaci\'f3\loch\f0 \hich\f0 n de los pesos seg\'fa\loch\f0 n la regla de Hebb.
\par \hich\af0\dbch\af31505\loch\f0 \hich\f0 La minimizaci\'f3\loch\f0 n de J es equivalente al logaritmo negativo de la probabilidad del residuo, e, si e es la Gaussiana y es igual a maximizar la\hich\af0\dbch\af31505\loch\f0  probabilidad del residuo.
\par \hich\af0\dbch\af31505\loch\f0 \hich\f0 Permite al residuo tener una funci\'f3\loch\f0 n de densidad de probabilidad:}{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\insrsid13593770 
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\par }{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\insrsid13593770\charrsid14683089 \hich\af0\dbch\af31505\loch\f0 \hich\f0 Luego denotamos una funci\'f3\loch\f0 n de coste general asociada a la red como:}{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 
\f0\fs20\insrsid13593770 
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{\pict{\*\picprop\shplid1027{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}
\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw3986\pich776\picwgoal2260\pichgoal440\wmetafile8\bliptag1163333084\blipupi-201{\*\blipuid 45570ddc8aa36f0b8a03b71240077619}
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\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\insrsid13593770 
\par }{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\insrsid9779688\charrsid14683089 
\par }{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\insrsid13593770\charrsid14683089 \hich\af0\dbch\af31505\loch\f0 donde k es una constante. Real\hich\af0\dbch\af31505\loch\f0 izando gradiente descendente en J se obtiene:}{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 
\f0\fs20\insrsid13593770 
\par }{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\insrsid9779688\charrsid14683089 
\par }{\pard\plain \ltrpar\qj \li0\ri0\sa200\sl276\slmult1\nowidctlpar\wrapdefault\faauto\rin0\lin0\itap0\pararsid14683089 \rtlch\fcs1 \af0\afs20\alang1025 \ltrch\fcs0 
\fs20\lang3082\langfe3082\loch\af0\hich\af0\dbch\af31505\cgrid\langnp3082\langfenp3082\charrsid14683089 {\object\objemb\objw4221\objh620{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e3300000000000000000000120000
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\f0\fs20\insrsid11145427\charrsid14683089 {\pict{\*\picprop\shplid1028{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}}
\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw7444\pich1094\picwgoal4220\pichgoal620\wmetafile8\bliptag-1271929157\blipupi-490{\*\blipuid b42fe6bb6ea394a6ce87285fe6b745c0}
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\f0\fs20\insrsid13593770 
\par }{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\insrsid9779688\charrsid14683089 
\par }{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\insrsid13593770\charrsid14683089 \hich\af0\dbch\af31505\loch\f0 donde T es la traspuesta del vector. }{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\insrsid9779688 
\par 
\par }\pard \ltrpar\qj \li0\ri0\sa200\sl276\slmult1\nowidctlpar\wrapdefault\faauto\rin0\lin0\itap0\pararsid4604842 {\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\insrsid13593770\charrsid14683089 \hich\af0\dbch\af31505\loch\f0 \hich\f0 
Se debe esperar que para residuos leptoc\'fa\hich\af0\dbch\af31505\loch\f0 \hich\f0 rticos (con mayor curtosis que una distribuci\'f3\loch\f0 \hich\f0 n Gaussiana), valores de p<2 deber\'ed\loch\f0 \hich\f0 
an ser apropiados, mientras que para residuos mesoc\'fa\loch\f0 \hich\f0 rticos (menor curtosis que la Gaussiana), valores de p>2 ser\'e1\loch\f0 \hich\f0 n los apropiados. Es com\'fa\loch\f0 n creer que es menos importante obte
\hich\af0\dbch\af31505\loch\f0 n\hich\af0\dbch\af31505\loch\f0 \hich\f0 er exactamente la distribuci\'f3\loch\f0 \hich\f0 n correcta cuando se busca para una fuente espec\'ed\loch\f0 \hich\f0 fica, que obtener una distribuci\'f3\loch\f0 \hich\f0 
n correcta aproximada, es decir todas las se\'f1\loch\f0 \hich\f0 ales supergausianas pueden conseguirse utilizando una distribuci\'f3\loch\f0 \hich\f0 n gen\'e9\loch\f0 \hich\f0 rica leptoc\'fa\loch\f0 rtica, y todas l\hich\af0\dbch\af31505\loch\f0 a
\hich\af0\dbch\af31505\loch\f0 \hich\f0 s se\'f1\loch\f0 \hich\f0 ales subgausianas pueden conseguirse  utilizando una distribuci\'f3\loch\f0 \hich\f0 n gen\'e9\loch\f0 \hich\f0 rica mesoc\'fa\loch\f0 rtica.
\par }\pard \ltrpar\qj \li0\ri0\sa200\sl276\slmult1\nowidctlpar\wrapdefault\faauto\rin0\lin0\itap0\pararsid14683089 {\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\insrsid13593770\charrsid14683089 \hich\af0\dbch\af31505\loch\f0 \hich\f0 
Los experimentos realizados tienden a soportar esta creencia para alguna proporci\'f3\loch\f0 \hich\f0 n, pero a menudo se obtiene precisi\'f3\hich\af0\dbch\af31505\loch\f0 \hich\f0 
n y es mejor la velocidad de convergencia cuando se consigue mayor precisi\'f3\loch\f0 \hich\f0 n en la elecci\'f3\loch\f0 n de p.
\par \hich\af0\dbch\af31505\loch\f0 Luego vemos como son las operaciones de la red:
\par \hich\af0\dbch\af31505\loch\f0 \hich\f0 Feedforward o alimentaci\'f3\loch\f0 n hacia delante:}{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\insrsid9779688\charrsid14683089 
\par }{\pard\plain \ltrpar\qj \li0\ri0\sa200\sl276\slmult1\nowidctlpar\wrapdefault\faauto\rin0\lin0\itap0\pararsid14683089 \rtlch\fcs1 \af0\afs20\alang1025 \ltrch\fcs0 
\fs20\lang3082\langfe3082\loch\af0\hich\af0\dbch\af31505\cgrid\langnp3082\langfenp3082\charrsid14683089 {\object\objemb\objw1620\objh700{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e3300000000000000000000100000
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\sectd \ltrsect\linex0\sectdefaultcl\sftnbj {\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\insrsid599539 
\par 
\par }{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\insrsid13593770\charrsid14683089 \hich\af0\dbch\af31505\loch\f0 \hich\f0 (Fyfe y McDonald, 2001) usan un solo valor de p (p=1) en esta regla  y describen este m\'e9\loch\f0 \hich\f0 
todo realizando un tipo de PCA, pero esto no es estrictamente cierto ya que s\'f3\loch\f0 \hich\f0 lo la regla Hebbiana original realiza PCA. Puede parecer m\'e1\loch\f0 s a\hich\af0\dbch\af31505\loch\f0 \hich\f0 
propiado unir esta familia de reglas de aprendizaje al An\'e1\loch\f0 \hich\f0 lisis de Factores Principales, ya que este m\'e9\loch\f0 \hich\f0 todo hace una suposici\'f3\loch\f0 
n sobre el ruido en un conjunto de datos y luego elimina el ruido de la estructura de covarianza de los datos, antes de realizar \hich\af0\dbch\af31505\loch\f0 P\hich\af0\dbch\af31505\loch\f0 \hich\f0 CA. Se hace algo similar aqu\'ed\loch\f0 \hich\f0 
, ya que se basa en la regla tipo PCA en la distribuci\'f3\loch\f0 \hich\f0 n supuesta del residuo. Maximizando la probabilidad del residuo con respecto a la distribuci\'f3\loch\f0 \hich\f0 n actual, se est\'e1\loch\f0 
 asociando la regla de aprendizaje al pdf del residuo.
\par \hich\af0\dbch\af31505\loch\f0 \hich\f0 M\'e1\loch\f0 s imp\hich\af0\dbch\af31505\loch\f0 \hich\f0 ortante es enlazar este m\'e9\loch\f0 \hich\f0 todo al m\'e9\loch\f0 \hich\f0 todo est\'e1\loch\f0 \hich\f0 ndar estad\'ed\loch\f0 \hich\f0 
stico de EPP: ahora la naturaleza y cuantificaci\'f3\loch\f0 \hich\f0 n de lo interesante es en t\'e9\loch\f0 \hich\f0 rminos de c\'f3\loch\f0 \hich\f0 mo probables son los residuos bajo un modelo particular de pdf de los residuos. Tambi\'e9\loch\f0 
\hich\f0 n se \'93\loch\f0 \hich\f0 blanquean\'94\loch\f0  los dat\hich\af0\dbch\af31505\loch\f0 o\hich\af0\dbch\af31505\loch\f0 \hich\f0 s antes de aplicar el m\'e9\loch\f0 \hich\f0 todo de aprendizaje y con este m\'e9\loch\f0 \hich\f0 todo tambi\'e9
\loch\f0 n se encuentran estructuras interesantes en los datos.
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